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How to Calculate the Area of Composite Figures

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How to Calculate the Area of Composite Figures

In this particular lesson let’s learn how to compute area of composite figures. Composite figures are figures that are made up of two or more figures. So the first problem says, “Find the area of the figure and this are the figure given to us.” What I am going to do is break this figure up into two rectangles. So this is rectangle 1 and this is the rectangle 2 – really easy right?

So the area of the composite figure = area of rectangle 1 + area of rectangle 2 very simple right? Rectangle 1, rectangle 2 if add the areas of both them, I should get the area of the entire figure. So what is area of rectangle 1?

Rectangle 1 is right here, that is length x width is 8 x 3 cm square. 8cm x 3cm, cm x cm = cm square. 8 x 3 = 24 so this is 24cm square. What is the area of rectangle 2?

Rectangle 2 is again length x width, is length is 6cm x the width which is 4cm. 6 x 4 = 24 cm x cm is 24cm squared, so both area 1 and area 2, rectangle 1 and rectangle 2 have the same area of 24 and 24. So the total area of the composite figure is this sum of both of them so area of the composite figure is 24cm square + 24cm square which is 24 + 24 = 48cm square that is what we are looking for. Area of the composite figure is 48cm square. All I did was breaking it up into two rectangles and added the areas of the individual ones.

Now crawl down a little bit and try the second problem. Second problem wants us to find the shaded area here. As I can see, I got two figures here. I’ve got the rectangle so I got the area of a rectangle which is the complete box. This is equal to area of the shaded region which is this part + area of triangle. The rectangle is made up of the triangle which is not shaded and the rest of the area which is shaded. So what do we need, what do we know, let’s see what we know area of the rectangle? Can we figure this out? Area of the rectangle is length x width.

Length is 12cm x the width is 8cm, so the area of the rectangle is 12 x 8 = 96cm square. This is = area of the shaded region that is what we need to compute, plus can we find the area of the triangle. What do we know about the triangle, the area is ½ x base x height that is the formula? So ½ x do we know the base, the base of the rectangle and the triangle are the same. They are exactly the same, so it is 12cm x the height which is given to us as 4cm.

So the area of a triangle is half x 12 x 4 = 24cm square. So I am going to take a little and what we know so far. We know that the area of the rectangle which is 96cm square is – to area of the shaded region + 24cm square. So if I want to find out what this is, I can subtract – 24cm square from both sides. And get this and this is 0, so the area of shaded region + 0 = 96 – 74 = 27cm square. Or the area of the shaded region is 72cm square, this is 72cm square.

What did I do to know to compute that, I have realized that I could take the area of the rectangle which is equal to the area of the shaded region which is I want to find out. And the area of the triangle which is right here—this part. So since we could compute the area of the rectangle using the formula length x width and the are of the triangle is half x base x height. And all of these are given to us; all we needed to do was use this to get the area of the shaded which had been 72cm square.

TenMarks is a new education initiative which aims to change the way kids learn. The company was founded by parents who believe that is a better way to help their (and all) kids build a strong foundation in math. The curriculum and the lessons are crafted and reviewed by experienced educators. The TenMarks educational advisory council guides the company to path-breaking innovation in education.